BENGHAZI, Libya (Reuters) - Libya's elected parliament voted on Monday to suspend its participation in a U.N.-sponsored dialogue between Libya's rival conflict parties, vying for control of the oil producer, lawmakers said.

The United Nations had been planning to hold a new round of talks in Morocco this week, the latest attempt to defuse a violent power struggle threatening to break up the North African country.

The elected assembly has been based in the east, like the internationally recognised government, since a faction called Libya Dawn seized the capital Tripoli in August, reinstating the previous assembly and installing a rival government there.

Farraj Hashem, spokesman of the House of Representatives, cited a double suicide bombing claimed by Islamic State militants in the eastern town of Qubbah on Friday, which killed 45 people, as a reason for the suspension:

"The other side did not condemn the Qubbah blast and does not acknowledge the terrorism on its land."

He also said the dialogue lacked any "vision".

Opposition to the U.N.-sponsored talks has been building in the east. Some lawmakers have accused Libya Dawn of having ties to Islamist militants, something it denies.

On Friday, several hundred protesters in the main eastern city, Benghazi, demanded an end to the talks, burning the flags of the United States and Britain and accusing them of backing Islamist groups.

Another lawmaker, Idris Abdullah, said there were concerns that the talks would lead to a national government approved by both parliaments, which might undermine the legitimacy of the House of Representatives.

The United Nations has been trying to form such a unity government to end the political splits.

But each side encompass a variety of political and business leaders as well as armed groups, unsurprising in a country left without effective national institutions by Muammar Gaddafi's 42-years of one-man rule.

The other rival assembly, the General National Congress in Tripoli, said it was willing to continue the dialogue, which started in September in the southern Libyan city of Ghadames, a lawmaker who asked not to be named told Reuters.

Each side is backed by brigades of fighters who helped to oust Gaddafi in 2011 but have since turned against one another in a complex conflict involving tribes, former Gaddafi troops, Islamist militants and federalist forces.